2.29: Exponential displacement and rest

0606/21/O/N/20 — Question 9 · 8 marks

A particle moves in a straight line such that, tt seconds after passing a fixed point OO, its displacement from OO is ss m, where s=e2t10et12t+9s = \mathrm{e}^{2t} - 10\mathrm{e}^{t} - 12t + 9.
(a)
Find expressions for the velocity and acceleration at time tt.
[3]
(b)
Find the time when the particle is instantaneously at rest.
[3]
(c)
Find the acceleration at this time.
[2]